SOLUTION: 8 sin 6x + 8 sin 2x = 0 I have found the answers pi/2, pi/4+pi/2 and have failed to get the correct answers when typing them into my homework system (Cengage). If anyone can hel

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Question 1169221: 8 sin 6x + 8 sin 2x = 0
I have found the answers pi/2, pi/4+pi/2
and have failed to get the correct answers when typing them into my homework system (Cengage).
If anyone can help, I would greatly appreciate it.
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!

The equation y = 8sin(6x)+8sin(2x) has zeros at for n in {Z} (n = 0,+/-1,+/-2,+/-3, etc.)
Answer by ikleyn(52943)   (Show Source): You can put this solution on YOUR website!
.

The given equation

    8*sin(6x) + 8*sin(2x) = 0     (1)


is equivalent to this one

    sin(6x) + sin(2x) = 0         (2)


(after canceling the factor 8).


In the plot below I show the left side function of equation (2) on the interval [0,2pi).



    


                 Plot  y = sin(6x) + sin(2x)



From the plot, you see that there are 8 roots (solutions) on the interval [0,2pi).


To find all these solutions, you need to solve these equations

    6x = 2x,          (3)

    6x = 2x +      (4)

    6x = 2x +     (5)

    6x = 2x +     (6)

    6x = 2x +     (7)

    6x = 2x +     (8)

    6x = 2x +     (9)

    6x = 2x +     (10)


Equations (3)- (10) give the solutions x such that 6x and 2x differ in :  then sin(6x) and sin(2x) have the opposite signs.



The solution of these equations is ELEMENTARY, and I leave it to you.


When you complete your calculations, COMPARE the found roots with that you see in the plot.

------------

You are guided, explained, directed and instructed.



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